Mann iterative process for pseudocontractive mappings

Let K be a nonempty, closed and convex subset of a real Banach space E. Let T:K→K be a strictly pseudocontractive map. For a fixed x ₀∈K, define a sequence {x _n } by x _n+1=(1?α _n )x _n +α _n Tx _n , where {α _n } is a real sequence defined in 0,1] satisfying the following conditions (i) $\sum_{n=0}^{\infty }\alpha _{n}=\infty $ , (ii) lim? _n→∞ α _n =0. Then lim?inf? _n→∞‖x _n ?Tx _n ‖=0. If, in addition, T is demicompact, then {x _n } converges strongly to some fixed point of T. Remark 8 is important.